Noninner Automorphisms of Order p of Finite p-Groups
نویسندگان
چکیده
منابع مشابه
Finite P-groups of Class 2 Have Noninner Automorphisms of Order P
We prove that for any prime number p, every finite non-abelian p-group G of class 2 has a noninner automorphism of order p leaving either the Frattini subgroup Φ(G) or Ω1(Z(G)) elementwise fixed.
متن کاملEXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER p FOR FINITE p-GROUPS
In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order p for a finite non-abelian pgroup. Among other results, we prove that if G is a finite non-abelian pgroup, p is odd and G/Z(G) is powerful then G has a noninner automorphism of order p. To prove the latter result we show that the Tate cohomology Hn(G/N, Z(N)) 6= 0 for all n ≥ 0, where G i...
متن کاملA Note on Absolute Central Automorphisms of Finite $p$-Groups
Let $G$ be a finite group. The automorphism $sigma$ of a group $G$ is said to be an absolute central automorphism, if for all $xin G$, $x^{-1}x^{sigma}in L(G)$, where $L(G)$ be the absolute centre of $G$. In this paper, we study some properties of absolute central automorphisms of a given finite $p$-group.
متن کاملnoninner automorphisms of finite p-groups leaving the center elementwise fixed
a longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. let $g$ be a finite nonabelian $p$-group. it is known that if $g$ is regular or of nilpotency class $2$ or the commutator subgroup of $g$ is cyclic, or $g/z(g)$ is powerful, then $g$ has a noninner automorphism of order $p$ leaving either the center $z(g)$ or the frattin...
متن کاملnoninner automorphisms of finite $p$-groups leaving the center elementwise fixed
a longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. let $g$ be a finite nonabelian $p$-group. it is known that if $g$ is regular or of nilpotency class $2$ or the commutator subgroup of $g$ is cyclic, or $g/z(g)$ is powerful, then $g$ has a noninner automorphism of order $p$ leaving either the center $z(g)$ or the frattini subgro...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9093